I canned 4 quarts of applesauce tonight, and as I pulled them from the waterbath, there was air in the bottles (not there when I stuck them in) and sauce around the rims and down the bottles. What happened? 3 have sealed so far, and I'm waiting for the 4th. Will they be safe?

I think you overfilled your jars. You need at least a half inch of air above the applesauce when you can it, because it's going to boil and expand in there while you process it. As long as they seal, I think they'd still be okay, but I'm not a canning expert.

you overfilled the jars. Applesauce needs 1/2" headspace and as long as the jars seal you are OK. Just be sure to wash the outside of the jar before storing.

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Yep, I agree. I think you've over filled you jars. Also, siphoning can happen when you pull them out and there is too great a difference between the temp of the water and the temp of the air in you kitchen. I've had it happen with jars that weren't over filled before. Just cover you jars as you take them out with a towel. This will slow the cooling process and help with siphoning issues.